1. Field of Invention
This invention relates to a flowmeter for measuring mass flow of generally fluent materials such as liquids, wherein the induced Coriolis force on the components of the flowmeter is correlated to a measurement of mass flow.
2. Description of Related Art
Mass flowmeters (or direct mass flowmeters) have sensing means which respond to mass flow rate as compared to volume flow rate. Other types of flowmeters employ, for example, sensing means which respond to differential pressure or fluid velocity. If a need arises to measure mass flow rate with such devices, a separate measurement of fluid density must be performed and an inference made about the flow distribution pattern in the cross section of the meter. Thus for reason of measurement simplicity alone, direct mass flowmeters are very desirable.
In practice, the mass flow measurement is much more useful than other types of flowmeters which measure volume flow rate because chemical reactions require blending of proportional mass (not volume) of ingredients and product specifications generally refer to mass percentage of ingredients rather than volume percentage. Thus the ability to measure mass flow directed rather than volume flow represents a major advantage of direct mass flow measurement over other techniques.
Coriolis flow meters (CFM's) are direct mass measuring flowmeters. They detect the Coriolis force and use the influence of a pattern (or couple) of such forces upon flow tubes carrying the fluid within the meter. Devices disclosed to date employ one or two flow tubes which may split the fluid stream and carry a fraction of the flow of fluid or may carry the fluid stream serially through both tubes. The flow tubes are typically vibrated by a magnetic force coupling between a drive coil and a permanent magnet. The flow tubes are driven at their resonant natural frequency in a given mode of vibration. Coriolis forces are generated between the fluid and the vibrating tubes. The forces are proportional to the mass flowrate within the tubes. The sum of the moments produced by the distributed Coriolis forces cause the tubes to be twisted or deflected in opposition to the normal motion that the tubes would have at zero flowrate. The twisting can be measured as a time delay or a phase shift in the relative motion of the tubes. The time delay, or phase shift is proportional to the mass flowrate.
U.S. Pat. No. 3,276,257 describes a prior art mass flowmeter that operates using Coriolis forces. The mass flowmeter described in that patent consists generally of a circular tube (forming a reference plane) that is excited to vibrate in a direction normal to the reference plane in which it is at rest. The fluid whose mass flow rate is to be measured is made to flow through the vibrating tube. The Coriolis force couple on the tube resulting from the fluid flow causes the tube to twist. For a given geometry and amplitude of induced vibration, the angle of twist of the tube induced by the Coriolis force couple is proportional to the true mass flow rate. The angle of twist is determined by the time difference between the instant that one side of the tube crosses a given reference plane and the instant that the opposite side crosses the same reference plane. To accomplish this measurement, two sensors are mounted on opposite sides of a pipe, through which the fluid flows in opposite directions. A phase shift is measured between the output of two sensors. This phase shift is proportional to the Coriolis force couple accelerating the tube, and therefore proportional to the mass flow through the meter.
The designation of the Coriolis forces as "couples" is inherent in the structure of the flow tubes in a meter. For each part of a flow tube which is, during the vibration of the tube, not parallel with the axis of motion (rotation) of the vibrated tube, a Coriolis force is produced. The force acts through the body of the fluid, which in turn will produce pressure on the flow tube wall, thereby inducing motion in the tube itself. The magnitude of the Coriolis force is proportional to the mass flow rate, the angular velocity of rotation, the sine of the angle between flow direction within the element and the direction of the rotation vector. The Coriolis force typically becomes a force couple because the one flow tube has regions with opposite flow directions of fluid flow. In the regions of the tube where the flow is in opposite directions, two Coriolis forces concurrently applied to the structure will be in opposite directions, therefore the term "force couple" is generally employed.
As used above, and throughout this application, the term "motion" is used to describe change in position, velocity, and acceleration of a point or aggregate of points on the flow tube(s) or any time-derivative or time-integral of these variables. Motion is observed over the time of a typical single oscillatory cycle while performing a flow measurement. The flow tube's motion is periodic and any one of these physical variables for any point on the flow tube can be determined.
Another concept in this application describes the induced vibratory motion in the flow tubes of the Coriolis flowmeter. This is the requirement that the vibration of the fluid carrying tubes be maintained at a "natural frequency" of a mode of free (unforced) vibration.
The tubes are driven at the natural frequency in a Coriolis mass flowmeter. This requires that the periodic driving force lag the periodic displacement of the flowtube by precisely 90.degree.. In other words, the periodic force and the motion can be described by the following equations: EQU X=X.sub.O sin (.omega.t) (1) EQU F=F.sub.O cos (.omega.t) (2)
where
X=Deflection from the neutral plane (displacement) PA1 X.sub.O =Maximum deflection PA1 F=Periodic driving force PA1 F.sub.O =Maximum value of the periodic force PA1 .omega.=Frequency of vibration, radians/sec PA1 t=Time, seconds
U.S. Pat. No. 3,355,944 to Sipin expands on the above concepts. Here, a U-shaped tube is vibrated about an axis in the plane formed by the tube, passing through the open ends of the U section. When a liquid material flows through the tube, a Coriolis force couple acts on the inlet and the outlet sections of the tube (the legs of the U) located at right angles to the axis about which the tube is vibrated. This couple is caused by the Coriolis force being induced because of the opposite direction of flow of the material in these inlet and outlet sections. This force couple twists (or torques) the U-shaped tube about an axis which is in the plane defined by the U-shaped tube, and which is parallel to the inlet and outlet sections and equidistant between them. As the U-shaped tube is vibrated back and forth, the Coriolis force couples will oscillate back and forth as the angular velocity alternatively reverses direction.
The Sipin Patent describes a one tube Coriolis flowmeter design. There is a distinction between Coriolis flow meters of one and two tube design. An example of a two tube design is shown is U.S. Pat. No. 4,192,184 to Cox et al, issued Mar. 1, 1980. In the two tube design, the tubes are symmetrical and the measurement of flow tube deflection and motion is done between the two vibrating tubes, i.e. the reference for performing the measurements on one tube is the other tube. Conversely, a single flow tube device must use a reference which is not a tube containing fluid to be measured. The reference can be a tube without process fluid, or some other stationary object. Because the reference is critical in any measurement, a major consideration in single tube units is mounting requirements to eliminate influences from floor vibrations or pressure pulsations in the process fluid.
As the Cox Patent describes, in the two tube design, depending on direction of flow, when the tube pairs are induced to vibrate, they will alternately come close together to a minimum spacing, and then separate to a maximum spacing. Therefore, the angular velocity vector for one tube will always be opposite from the angular velocity vector of the other tube. If the flow through the two tubes is the same, that is if the flow near the inlet sections are both in a first direction, and the flow near the outlet sections are both in an opposite direction, then each of the tubes will be subject to opposing torques with respect to an axis in the plane formed by the tube. This effect is caused because of the opposite angular velocity vectors in the inlet and outlet of the tubes. This two tube arrangement cancels any net Coriolis induced force on the mounting means for the tube pairs.
To better explain the motion in the two tube design, and illustrate relevant flow tube motion in the present invention, FIG. 1, corresponds to FIG. 1 of the Cox Patent, with renumbered elements and shows the fluid elements of a dual U-tube Coriolis flowmeter having parallel flow paths. The ends of each U-tube are rigidly attached to a support block 100. After the fluid passes through the first U-tube 102, a return connection 104 within or attached to the support block 100 allows the fluid to enter the second U-tube 106. The return connection 104 is configured such that the fluid flow paths are parallel in each U-tube 102, 106.
Typically, velocity or displacement sensors 110, 112 are attached between, and on, each leg of the "U-tubes". The difference in the displacement measured by the two sensors is proportional to the relative angle of twist of the two U-tubes 102 and 106.
An electromagnetic driver 108 is attached between the ends of the two "U-tubes" to vibrate the tubes in opposite directions to each other at the natural resonant frequency of the tubes. A phase locked loop (PLL) feedback system is used to precisely drive the oscillating means to induce vibrations in the "U-tubes" at (or near) their resonant frequency. A detailed description of a known means for driving and sensing the motion of flowmeter tubes in a Coriolis type flowmeter is described in U.S. Pat. No. 4,814,680 to Hulsing issued Mar. 21, 1989.
The U-tube motion of the tubes in FIG. 1 under the influence of the Coriolis force is detailed in FIG. 1A. Here, the end view of the tubes shows the effect of a finite acceleration and deceleration due to the Coriolis couple created by the fluid flowing through the tubes causing the U-tubes to twist in opposite directions to each other. The sensor axis in FIG. 1A shows where sensors 110, and 112 are placed to sense the changing distance between the tubes. The driver axis, is where driver 108 is placed to induce vibratory motion in tubes 102, 106.
The explanation of the motion of the tubes in FIG. 1A is best understood by the introduction of two reference planes associated with the two flow tubes shown in FIG. 1. Plane A is defined by (top) flow tube 106, while plane B is defined by (bottom) flow tube 102. Both planes pass through the center of the tubes 102, 106. Both planes are, at the instant represented by FIG. 1A, 2X apart with the distance X corresponding to one half the spacing between tubes 102 and 106 when they are not being vibrated, i.e. at rest. Distance X at this instant of time also defines plane C, which is equispaced from planes A and B, and parallel to them. The mounting distance X between the two U-tubes shown in FIG. 1A is not particularly important--the tube deflections away from the neutral plane are. Because of the instant of time FIG. 1A represents, and the definition of planes A and B, the distance 2X also corresponds to the mounting distance 2X between the centers of tubes making up flow tubes 102 and 106, and shown with respect to block 100 in FIG. 1.
When the vibrating tube 102 or 106 passes through their respective neutral planes, the motion of each element of the tubes is at the maximum velocity in the periodic motion the tube. At the same time, the maximum angular velocity of the tubes is attained. The magnitude of the distributed Coriolis forces is also at a maximum when the vibrating tubes pass through their respective neutral planes A or B.
The periodic forces which drive the tubes 102 and 106 at their resonant frequency, cause the tubes to deflect approximately 2,000 times the magnitude of deflection that the tubes would be subject to compared with the same forces applied as a static force. This is due to the relatively small amount of damping within the tube material. The Coriolis forces are also at a maximum when the tubes pass through the neutral plane, but the Coriolis forces are not at a resonance condition and the deflection produced by these forces is only 1 to 2 times the deflection that the Coriolis forces would produce as steady state forces. However, the twisting moment produced by the Coriolis forces is greater than the moment needed to drive the tubes in resonance. Consequently, the small amplification effect of the Coriolis forces is partially compensated by actually having a higher magnitude effect than the driving force under static conditions.
When the tubes 102, 106 are vibrated in a sinusoidal manner, and there is no flow in the tubes, the distance X will increase and decrease equally and uniformly between sensor axes, i.e. the sensed locations associated with sensors 110 and 112 will move up and down equally closer or further with respect to plane C. In this assumed no flow situation, the average distance X will correspond to the point at which the sinusoidal oscillating velocity of the tubes will be at its maximum.
Now a flow of material is assumed into the flow tubes. Assume the tubes at this instant are moving apart, and planes A and B would have been X away from C if there was no flow. Because of the Coriolis force couple, the locations associated with the axis of sensor 110 will move apart, away from plane C more than the expected distance X, while the location associated with sensor 112 will be closer to plane C than expected distance X.
The effect of the Coriolis force couple on tube 106 is to twist it counterclockwise as shown in FIG. 1A, while tube 102 is twisted clockwise. The reason the Coriolis force couples applied to tubes 102 and 106 are in different directions is because the instantaneous velocity vector of the tubes perpendicular to planes A and B is of opposite signs, i.e., tube 102 is moving in the opposite direction of tube 106 with respect to plane C. Since the fluid flow is in the same direction in both tubes 102 and 106 the Coriolis forces exercised on the tubes will be of opposite direction. This Coriolis force induced twisting shown in FIG. 1A is a periodic motion which occurs at the same frequency as the tube resonant frequency. When the U-tubes move away from each other, during the next half cycle of the periodic motion, the twisting due to the Coriolis force couple will be in the opposite direction, i.e. the spacing at sensor 110 will be a minimum while the spacing between 106 and 102 at 112 will be at its maximum.
This motion of the tubes can better be understood by referring to actual examples of physical characteristics of commercial U-tube type Coriolis flowmeters. As previously described, the true mass flow rate through the U-tubes is proportional to the relative angle of twist between the tubes. The magnitude of the deflections, shown in FIG. 1A, is exaggerated for illustration purposes. Under typical operating conditions, the maximum deflection at the ends of the U-tubes for a tube length of about 70 times its diameter, due the oscillatory motion alone, (the quantity X in FIG. 1A), is typically about 0.1 inches. In contrast, the relative deflection due to Coriolis force twisting is on the order of 0.005 inches.
Having completed the explanation of the effect of the Coriolis forces on the flow tubes, some other important factors of flowmeter operation will be considered.
First, pressure drop between the input and output of the flowmeter is a major factor in many Coriolis flowmeter applications and should be minimized. In order to keep the pressure drop across the flowmeter within the limits placed by the available pumping capacity in the line, it is necessary that the flowmeter does not introduce an excessive pressure drop, i.e. the meter should have a large diameter and short flow tube, or, in the alternative, multiple parallel flow tubes sharing the overall flow. This minimizes the pressure loss associated with the introduction of the meter in the path of the fluid flow.
Second, the size of the Coriolis flowmeter itself should be minimized. The primary disadvantage of the Coriolis flowmeters that are currently being manufactured for fuel custody transfer and the process control industry is that the flowmeters are large and heavy compared with other types of flowmeters. The reason for the large size and weight of the contemporary Coriolis flowmeters is that the flow paths through the U-tubes are in series. To keep pressure drops across the meter low, the tubing must be of large diameter. Once a large diameter tube has been selected, the tubes must be made long in order to achieve enough movement at the ends of the tubes to permit measurement of Coriolis induced deflection. Long length of the tubes implies a relatively large flowmeter size.
Third, the tolerance of the Coriolis flowmeter to interference from acoustic waves or external vibrations generated by pumps and other process equipment should be maximized. Such interference can cause considerable deterioration in the accuracies of Coriolis flowmeter measurements especially if these interfering vibrations are periodic and have frequencies close to those of the frequency induced by the Coriolis forces. In a high interference environment, the Coriolis flowmeter may lose the ability to distinguish between motion caused by such disturbance or from a flow rate change. It is therefore desirable to minimize meter sensitivity to such acoustic disturbances as well as typical vibrations encountered in an industrial environment.
Fourth, the meter should be capable of tolerating a wide range of operating temperatures. This implies two considerations. First, the pipes of the flowmeter constitute a tuned mechanical assembly whose resonant frequency is meant to be relatively stable for accurate measurements. Adding mass to an oscillatory system will change its natural frequency (detune the assembly). This means that when mass flow rate changes, or unknown tube mass changes are introduced, the flow readings will be affected. Such unknown mass changes can come from unknown amounts of condensate being deposited on the pipes of a flowmeter when the temperature of the flowmeter drops below the dewpoint of the surrounding environment. When this condition is reached, water will condense from the air onto the external surfaces of the tuned pipes. Condensation on the tubes would produce an imbalance in the vibration characteristics since the condensation would not be uniform and the tube vibration would cause the condensate to agglomerate as well as "dance" around the vibrating tubes. The unknown mass of the condensate is now added to the original mass of the pipes thereby detuning the assembly and introducing errors in the flowmeter.
The second aspect of tolerating a wide range of operating temperatures is the adjustment of the readout of the meter because of the changes in the structure of the Coriolis flowmeter related to temperature. As the temperature changes the pipes of the meter, their stiffness and therefore resonant frequency will change. This needs to be compensated for to assure that the readout of Coriolis force couple induced motion is properly correlated to the actual flow rates through the meter.